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DESIGN A FILTER FOR HARMONICS CAUSED BY NON-LINEAR LOAD AND
RESONANCE CAUSED BY POWER FACTOR CORRECTION CAPACITOR
NOR FAEZAH BINTI ADAN
A thesis submitted in
fulfillment of the requirement for the award of the
Degree of Master of Electrical Engineering
Faculty of Electrical and Electronic Engineering
Universiti Tun Hussein Onn Malaysia
JANUARY 2016
ii
I hereby declare that the work in this thesis is my own except for quotations and
summaries which have been duly acknowledged.
Student : __________________________________________________
NOR FAEZAH BINTI ADAN
Date : __________________________________________________
Supervisor : __________________________________________________
DR. DUR MUHAMMAD SOOMRO
iii
For my beloved mother and father
iv
ACKNOWLEDGEMENT
Alhamdulillah, praise be upon Him whom has given me a good health, body and mind to
complete this Projek Sarjana. I would like to express my sincere gratitude to
Dr. Dur Muhammad Soomro, my supervisor for the support and guidance given throughout the
duration of this project.
The co-operation given by the Faculty of Electrical and Electronic Engineering, UTHM
is also highly appreciated. Appreciation also goes to everyone involved directly or indirectly
towards the compilation of this thesis. Last but not least, thank you to all my friends and family
for the generous moral support given throughout completing this task.
v
ABSTRACT
The traditional approach to power factor correction (PFC) in industrial applications
involves installation of power factor correction capacitor banks (PFCC). However, with the
expanding use of non-linear equipment such as adjustable speed drives (ASDs), power
converters etc., power factor (PF) improvement has become difficult due to the presence of
harmonics generated by the non-linear equipment. The resulting capacitive impedance of
the PFCC may form a resonant circuit with the source inductive reactance at a certain
frequency, which is likely to coincide with one of the harmonic frequency of the load. This
condition will trigger large oscillatory currents and voltages that may stress the insulation
and cause subsequent damage to the PFCC and equipment connected to the power system
(PS). Besides that, high PF cannot be achieved due to power distortion. These have imposed
the need for an approach to PFC by addressing the harmonics problem. This project
analyzes both passive filter and shunt active power filter (SAPF) techniques to mitigate
resonance and overall harmonics in the PS through simulation using PSCAD software. A
test case is presented to demonstrate the applicability of the proposed techniques for
harmonics reduction and PFC at the same time. The implementation of SAPF together with
passive filter have resulted in significant improvement on both total harmonic distortion for
voltage (THDV) and total demand distortion for current (TDDI) with maximum values of
only 2.93% and 9.84% respectively which are within the IEEE 519-2014 standard limits.
In terms of PF improvement, the combined filters have excellently achieved the desired PF,
0.95 for firing angle, α values up to 40o.
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ABSTRAK
Bank kapasitor seringkali digunakan di industri untuk menambahbaik faktor kuasa. Namun,
dengan peningkatan penggunaan alatan-alatan tidak linear seperti pemacu kelajuan boleh laras
(ASDs), penukar kuasa dan sebagainya, penambahbaikan faktor kuasa menjadi lebih sukar. Ini
adalah kerana kehadiran harmonik yang dihasilkan oleh alatan-alatan tidak linear tersebut.
Bank kapasitor menghasilkan galangan kapasitif yang mungkin akan bertembung dengan
galangan induktif punca kuasa pada salah satu frekuensi harmonik yang dihasilkan oleh beban
lantas menyebabkan terjadinya resonan. Keadaan ini akan menyebabkan terhasilnya ayunan
besar arus and voltan yang akan menyebabkan kerosakan kepada penebat seterusnya bank
kapasitor dan alatan-alatan lain yang terdapat di dalam sistem kuasa. Selain itu, herotan kuasa
menyebabkan faktor kuasa yang tinggi tidak dapat dicapai. Oleh kerana itu, satu langkah perlu
diambil untuk penambahbaikan faktor kuasa dengan cara mengurangkan harmonik. Projek ini
telah menganalisis teknik passive filter dan shunt active power filter (SAPF) dalam
mengurangkan masalah resonan dan keseluruhan harmonik melalui simulasi menggunakan
perisian PSCAD. Satu kes ujian telah dibentangkan untuk menunjukkan kesesuaian teknik
yang telah dicadangkan dalam mengurangkan harmonik dan pada masa yang sama
meningkatkan faktor kuasa. Hasil implementasi SAPF dan passive filter telah menunjukkan
penambahbaikan yang tinggi terhadap jumlah keseluruhan herotan harmonik bagi voltan
(THDV) dan arus (TDDI), kepada hanya 2.93% dan 9.84% nilai maksimum yakni di bawah
paras yang ditetapkan oleh standard IEEE 519-2014. Dari segi penambahbaikan faktor
kuasa, gabungan kedua-duanya telah berjaya mencapai faktor kuasa sasaran iaitu 0.95
untuk firing angle, α dari 0o-40o.
vii
CONTENTS
TITLE i
DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENT iv
ABSTRACT v
CONTENTS vii
LIST OF FIGURES ix
LIST OF TABLES xii
LIST OF ABBREVIATIONS xiii
CHAPTER 1 INTRODUCTION 1
1.1 Background of study 1
1.2 Problem statement 2
1.3 Objectives of study 3
1.4 Scopes of study 3
1.5 Thesis outline 4
CHAPTER 2 LITERATURE REVIEW 5
2.1 Introduction 5
2.2 Related works 5
2.2.1 Test model 6
2.2.2 Passive filters 7
2.2.3 Active power filters 9
2.2.4 Hybrid active power filters 11
2.2.5 Phase shifting method 13
viii
2.3 PF correction (PFC) 14
2.4 IEEE Standard for Harmonic Control 15
CHAPTER 3 METHODOLOGY 17
3.1 Introduction 17
3.2 Circuit topology 17
3.3 Design circuit elements 18
3.3.1 Distribution system 18
3.3.2 PFCC 20
3.3.3 Passive filter 20
3.3.4 SAPF 21
3.4 Control techniques 22
3.4.1 Calculation of reference compensations
currents 22
3.4.1.1 P-Q theory 22
3.4.1.2 High pass filter 26
3.4.2 SAPF firing pulses generation 26
CHAPTER 4 RESULTS AND DISCUSSION 30
4.1 Introduction 30
4.2 Distribution system without PFCC 30
4.3 Distribution system with PFCC 33
4.3.1 Calculated PFCC 33
4.3.2 Effects of PFCC on distribution system 34
4.3.2.1 Reference distribution system 34
4.3.2.2 Main distribution system 35
4.4 Power filter implementation 37
4.4.1 Passive filter 37
4.4.2 Passive filter + SAPF 41
CHAPTER 5 CONCLUSION 44
REFERENCES 46
ix
LIST OF FIGURES
2.1(a)(b) STPF, DTPF - Shunt passive filters 7
2.2 5th, 7th, 11th and 13th order STF in plastic plant
distribution system
8
2.3 Single phase shunt active filter configuration 9
2.4 Block diagram of SAPF controller using p-q
theory
10
2.5(a)(b) STHF, DTHF in 3-phase distribution system 11
2.6 Hybrid filter system set-up 12
2.7 Phase shifting approach for VSDs PFC and
harmonics mitigation
13
2.8 Relationship between S, P and Q 14
2.9 Addition of capacitors to correct PF 14
3.1 Passive filter and SAPF topology 18
3.2 Distribution system 19
3.3 Calculation of current reference based on p-q
theory
22
3.4 PSCAD models for Clarke transformation 23
3.4(a) Vα calculation 23
3.4(b) Vβ calculation 23
3.4(c) Iα calculation 23
3.4(d) Iβ calculation 23
3.5
PSCAD models for p-q instantaneous power
components calculation and HPF to obtain px
and qx
24
3.5(a) p calculation 24
x
3.5(b) q calculation 24
3.6 PSCAD models for compensation current
calculation in α-β coordinates
24
3.6(a) Icα calculation 24
3.6(b) Icβ calculation 24
3.7 PSCAD models for compensation current
calculation in a-b-c coordinates
25
3.7(a) Ica calculation 25
3.7(b) Icb calculation 25
3.7(c) Icc calculation 25
3.8 HPF configuration 26
3.9 Filter current 27
3.10 Measuring the difference between actual filter
currents and reference currents
27
3.11 Generation of SAPF switches firing pulses 28
3.11(a) Reference signals 28
3.11(b) Interpolated firing pulses block 28
3.12 Reference signals fed to interpolated firing
pulses block
28
3.13 Actual firing pulses generated 29
3.13(a) S1 and S4 switches 29
3.13(b) S3 and S6 switches 29
3.13(c) S5 and S2 switches 29
4.1 Reference system, supply with Rs = 0.002Ω,
Ls = 0
31
4.2 Main system, supply with Rs = 0.002Ω,
Ls = 0.5mH
31
4.3
4.3(a)
4.3(b)
Lower fundamental current at supply at α = 60o
No PFCC
40 kVAR PFCC
35
35
35
4.4
4.4(a)
4.4(b)
Resonance occurrence at 5th harmonic at α = 60o
30 kVAR PFCC
40 kVAR PFCC
36
36
36
4.5
4.5(a)
Load fundamental current
30 kVAR PFCC
37
37
xi
4.5(b) 40 kVAR PFCC 37
4.6 Passive filter implementation 37
4.7 Passive filter performance at Q = 15 38
4.8 Passive filter, Q=15 - voltage and current
waveforms at α = 60o
39
4.9 Passive filter performance at Q = 20 39
4.10 Passive filter, Q=20 - voltage and current
waveforms at α = 60o
40
4.11 Passive filter performance at Q = 30 40
4.12 Passive filter, Q=30 - voltage and current
waveforms at α = 60o
41
4.13 Passive filter and SAPF implementation 41
4.14 Current and voltage waveforms after filters
implementation at α = 60o
42
4.14(a) Supply current against load current 42
4.14(b) PCC voltage against supply voltage 42
4.15 SAPF compensated current at α = 60o 43
xii
LIST OF TABLES
1.1 PF surcharge rate for users at 132kV and below 2
2.1 Voltage distortion limit 15
2.2 Current distortion limits for system rated 120 V
through 69 kV
16
2.3 Current distortion limits for system rated above
69 kV through 161 kV
16
2.4 Current distortion limits for system rated above
161 kV
16
4.1 Simulated results without PFCC 32
4.2 Voltage and current harmonics distribution on
main system
33
4.3 Reference system - Calculated PFCC 34
4.4 Main system - Calculated PFCC 34
4.5 Reference system with PFCC 35
4.6 Main system with PFCC 36
4.7 RLC values for passive filter 38
4.8 Passive filter and SAPF implementation 43
xiii
LIST OF ABBREVIATIONS
ωn Harmonic frequency
AC Alternating current
ASDs Adjustable speed drives
C Capacitor
CCA Conventional control algorithm
DC Direct current
DF Distortion factor
DPF Displacement power factor
DTHF Double tuned hybrid active power filter
DTPF Double tuned passive filter
FFT Fast Fourier transform
fo Fundamental frequency
fr Resonance frequency
HAPF Hybrid active power filter
HPF High pass filter
HVAC Heating, ventilating and air conditioning
L Inductor
P Active power
PC Personal computer
PCA Proposed control algorithm
PCC Point of common coupling
PE Power electronics
PF Power factor
PFC Power factor correction
PFCC Power factor correction capacitor
xiv
PLL Phase locked loop
PQ Power quality
PS Power system
Q Reactive power
R Resistor
ROF Reactance one-port filter
S Apparent power
SAPF Shunt active power filter
SCC Sinusoidal current control
SeAPF Series active power filter
SMPS Switched-mode power supplies
SPWM Sinusoidal pulse width modulation
STHF Single tuned hybrid active power filter
STPF Single tuned passive filter
TDD Total demand distortion
TDDI Total harmonic distortion for current
THD Total harmonic distortion
THDV Total harmonic distortion for voltage
TNB Tenaga Nasional Berhad
UPS Uninterruptible power supply
VSC Voltage source converter
VSDs Variable speed drives
CHAPTER 1
INTRODUCTION
1.1 Background of study
In the past, harmonics represented less of a problem due to the conservative design of power
equipment. When electronic power converters first became commonplace in the late 1970s,
many utility engineers became quite concerned about the ability of power system (PS) to
accommodate the harmonic distortion as the harmonics problems defy many of the
conventional rules of PS design and operation that consider only the fundamental frequency
[1]. Results of their concern have sparked the research that has eventually led to much of
the knowledge about all aspects of power quality (PQ).
Harmonics in PS is defined as a sinusoidal component of a periodic wave or
quantity having a frequency that is an integral multiple of the fundamental frequency.
Malaysia uses a 50 Hz fundamental frequency, thus a 3rd harmonic frequency will be 3
times 50 Hz, or 150 Hz. Likewise, a 5th harmonic frequency is 250 Hz and so on. The odd
integer harmonics frequencies (3rd, 5th, 7th and so on) are the most predominant [2-4]. The
waveform of electric power at generation stage is purely sinusoidal and free from any
distortion but this situation is hardly achievable at consumer’s end that has a lot of non-
linear equipment in operation.
Non-linear equipment like power electronics (PE) devices are the most significant
cause of harmonics and inter-harmonics. They generate harmonic frequencies by drawing
non-linear current waveforms. Rectifiers, adjustable speed drives (ASDs), soft starters,
2
electronic ballast for discharge lamps, switched-mode power supplies (SMPS), and heating,
ventilating, and air conditioning (HVAC) system using ASDs among the list of common
PE devices used which generate harmonics. Meanwhile, inter-harmonics are produced by
static frequency converters, cyclo-converters, induction motors & arcing devices. The
effects of harmonics on a PS include equipment premature failure and degradation, low
power factor (PF) [5], nuisance trips, resonance etc. Equipment affected by harmonics
includes transformers, motors, cables, interrupters, and power factor correction capacitors
(PFCC).
Large industrial equipment like transformers, induction motors, generators etc. are
among the equipment that may contribute to lower PF. Ideally, users would want to ensure
their PS to maintain a unity PF but it is not easily achievable especially for larger
commercial buildings or plants that have different sizes and types of loads. Lower PF
causes higher apparent power required by the equipment to achieve the same amount of
output. Thus, overloading the component. The continuous additional work if not mitigated
will shortens the life of the equipment. In worse cases, equipment may work excessively
beyond rated parameters and thus lead to total failure. In Malaysia, penalties will be charged
on users that fail to meet the PF requirement set by the Tenaga Nasional Berhad (TNB).
Table 1.1 shows the surcharge imposed on users with electricity supply below 132kV.
Table 1.1: PF surcharge rate for users at 132kV and below
PF requirement Surcharge rate
For every 0.01 less than 0.85 1.5 % of current bill
For every 0.01 less than 0.75 3 % of current bill
1.2 Problem statement
PFCC is commonly used in the industry to improve PF of the PS due to its lower cost.
However, when harmonics are present, the resulting reactive impedance of the PFCC may
form a resonant circuit with the source or system inductive reactance at a certain frequency,
which is likely to coincide with one of the harmonic frequency of the load. This condition
will trigger large oscillatory currents and voltages that may stress the insulation and cause
subsequent damage to the capacitor banks and equipment connected to the PS [6]. In order
3
to solve this issue and optimize the operating cost, a practical approach must be
implemented to reduce the problem to an acceptable level. In this case, harmonics filters
such as passive, active or hybrid can be applied at the point of common coupling (PCC) to
absorb the large oscillatory currents caused by resonance and reduces the overall current
and voltage harmonics.
From literature review, there are fewer references that are focused on mitigating
resonance effect caused by PFCC on the PS with harmonics presence. Therefore, this
project has been undertaken to study the harmonic amplification problem caused by PFCC
and the overall effects of harmonics on PF. The result of the study is used to develop the
necessary passive filter to reduce or eliminate resonance and also used to design an active
filter to reduce the other harmonic components in order to improve the PF.
1.3 Objectives of study
1) To simulate the effects of PF correction (PFC) on PS frequency.
2) To design passive and active power filter separately to mitigate harmonics and
resonance problem caused by PFCC.
1.4 Scopes of study
1) Simulation models are developed using PSCAD software.
2) The test case [7] consists of a bridge rectifier and an RL load.
3) Single tuned passive filter is designed to address the resonance problem.
4) Shunt active power filter (SAPF) is designed to address the other harmonic components.
5) P-Q theory is implemented to calculate the compensation reference current for the
SAPF.
4
1.5 Thesis outline
After the introduction section, the outline of the thesis is organized as follows;
Chapter 2 presents reviews of past researches on harmonic analysis of domestic and
industrial non-linear PS, application of harmonic filters to improve PF, mitigate harmonics
and harmonics resonance caused by non-linear loads and PFCC followed by a brief
introduction to PFC theory. The literature review is concluded with details of harmonic
limits outlined by IEEE 519-2014 standard.
Chapter 3 describes modeling of a 3 phase distribution system with non-linear load
and PFCC, passive filter and SAPF using PSCAD software. This chapter also includes
mathematical equations of PFCC and passive filter.
Chapter 4 discusses voltage and current harmonics caused by the non-linear load on
the distribution system with and without PFCC implementation. The results of the
implemented passive filter and SAPF are also presented.
In Chapter 5, the conclusions of the thesis are given and the future work studies are
proposed.
Finally all references used in this thesis study are presented.
5
CHAPTER 2
LITERATURE REVIEW
2.1 Introduction
This chapter presents reviews of past researches on harmonic analysis of domestic and
industrial non-linear PS, application of harmonic filters to improve PF, mitigate harmonics
and harmonics resonance caused by non-linear loads and PFCC followed by a brief
introduction to PFC theory. The literature review is concluded with details of harmonic
limits outlined by IEEE 519-2014 standard.
2.2 Related works
The traditional approach to PFC in industrial applications involves installation of PFCC.
But with the widespread use of non-linear loads, PF improvement has becoming more
difficult. It is known that a circuit consisting both capacitors (C) and inductors (L) will
generate resonance at a certain frequency [6]. For a purely sinusoidal PS, resonance may
not even happen, but not in the case where the PS contains harmonics profile whereby the
integral multiple of the fundamental frequency (fo) have a high probability to coincide with
the resonance frequency (fr).
6
Harmonics filter is essential in PS that contains harmonics profile drawn by the non-
linear loads. They are designed to provide a bypass for the harmonic currents, to block them
from entering the PS or to compensate them by locally supplying harmonic currents and/or
harmonic voltages. Different methods have been proposed to overcome harmonics and
harmonics resonance such as by using passive filter, active power filters, hybrid active
power filters (HAPF) and other method like phase shifting approach.
2.2.1 Test model
Prior to developing a solution to eliminate the harmonics and its adjacent effects, it is
critical to identify the harmonics profile produced by each of the non-linear loads and also
the overall harmonics profile at PCC. Studies conducted by [7-8] have developed several
simulation models of typical domestic and industrial non-linear loads. It is more convenient
to perform harmonics analysis using computer simulation given the system components are
modeled accurately. Models developed in [7] include television, refrigerator, washing
machine, battery charger, lamps, fans, air-conditioner, antenna using servomotors, air
heating unit, adjustable speed drive (ASD) and uninterruptable power supply (UPS) which
were implemented to estimate the harmonics characteristics of a distribution system of
CARTOSAT-2A satellite launching station at ISRO, Bangalore, India.
On the other hand, research conducted in [8] performed harmonic analysis on a
residential house, small residential area and a small-scale industrial supply system. The
study concluded that, a residential house having all types of electronics and electrical home
appliances performed within the total harmonic distortion for voltage (THDV), and total
demand distortion for current (TDDI) limits respectively. Analysis performed on a small
residential area consisting three villages have shown that Village 2 and 3 with lower income
residents, did not contribute to high harmonics compared to Village 1 as they can’t afford
expensive equipment like air-conditioners, water heaters, dryer etc. Village 1 produces
acceptable TDDI but high THDV (9.4%) thus requires harmonics filter to reduce the voltage
harmonics. Meanwhile, harmonics analysis performed on the small-scale industrial supply
system, which comprises of ASDs, DC motors, arc welders, cyclo-converter, personal
computer (PC), air conditioners, fans and lamps resulted in both THDV and TDDI
exceeding the limits at 6.1% and 61.6% respectively.
7
Based on [8], it is profound to assume that an office building may also produce high
THDV as the equipment used is similar to residential houses while mechanical and electrical
laboratories in the university which has a close resemblance to the small scale industrial
system may also exceed both its TDDI and THDV limits. Therefore, harmonics filters are
definitely required to reduce the total harmonic distortion (THD) to an acceptable level.
2.2.2 Passive filters
Passive filters can be broadly classified into two types, series and shunt filter. Series filters
with high series impedance are used to block the relevant harmonic currents. Therefore
they must carry the full load current and be insulated for full line voltage. On the other
hand, shunt filters are used to divert the relevant harmonic currents to the ground by
providing a low impedance bypass path. The latter carry only a fraction of the current that
a series filter must carry, making the cost cheaper, thus more attractive to users [9-10].
Figure 2.1 illustrates the configuration of single tuned passive filter (STPF) and double
tuned passive filter (DTPF). STPF is specifically designed to eliminate distortion of one
harmonic order only while DTPF as the name imply, eliminates two harmonics components
simultaneously.
(a) STPF (b) DTPF
Figure 2.1: Shunt passive filters
The research in [11] focused on designing passive filters to mitigate harmonics
problem on a small-scale industrial loads i.e. 13-bus medium voltage industrial distribution
system. Similar non-linear models in [7-8] were adopted. Two types of passive filters were
designed and discussed in this paper, single/double tuned passive filter (STPF / DTPF) and
reactance one-port (ROF) arrangement. ASDs loads were connected to bus 7 and 10, PFCC
connected to bus 3 and active filter connected at PCC. Initial simulation with the PFCC
offline and no filters application has shown that both the ASD load buses exceeded the 5%
8
and 20% THDV and TDDI limits with 6.1% and 7.3% THDV and 24.9% and 26.2% TDDI
respectively. The other buses monitored include bus 3 and 9 with bus 3 readings well below
the limits and bus 9 exceeds TDDI limits at 25.6%. It was found that DTPF reduces THD
better than STPF. The researcher has also simulated the effect of PFCC to the distribution
system. As expected, the THD level is higher when PFCC is energized.
The simplicity and cost-effective of STPF are the main reasons why they are often
installed to mitigate harmonic problem. However, they are not always the most practical
solution. A study conducted by [12] have identified that STPF can be a culprit to harmonic
amplification. The problem started when four STPFs of 5th, 7th, 11th and 13th were
commissioned as shown in Figure 2.2, many cases of STPF capacitor failures were
reported. Through computer simulation, it was found that there was a parallel resonance
between the LC filters and the PS. Simulation on different filter structures have also shown
that the resonant frequency varied accordingly i.e. 4th order harmonic were amplified when
the 13th order filter was disconnected and both 4th and 8th order harmonic decreases
reasonably when the 11th and 13th order STPFs were offline. It was concluded that the filter
set-up were not suitable for a PS experiencing very infrequent unequal loading condition
and thus proposed a more practical solution, a 17th and 35th order high pass damped filters
as replacement to the original set-up.
Figure 2.2: 5th, 7th, 11th and 13th order STPF in plastic plant distribution system
The system parameters are dynamically changed according to the power system
configurations and loads. Therefore, even with passive filters implemented other harmonics
problems can still appear which means for a wider range of harmonic frequencies, an STPF
or DTPF alone is not sufficient to reduce the THD.
9
2.2.3 Active power filters
Active filters are the new trend in harmonic filtering technology. They make use of power
electronic switches and advanced control techniques. Hence, their responses are much
quicker than passive filters. The basic principle of operation of an active filter is to inject a
suitable non-sinusoidal voltage and current into the system in order to compensate the
harmonic contents. Active filters are still characterized by their relatively high cost
compared to the cost of passive filters [13]. According to their connection to the network,
active filters can be a series type (SeAPF), which prevents the transfer of harmonic current
or the shunt type (SAPF), which reduces harmonic content in the network.
The function of passive series filter and SeAPF is identical and thus faced the same
issues related to higher implementation cost especially for application in severe harmonics
conditions. Mainly because they must be designed to withstand the full load current and
full line voltage. In order to make it more practical, it has to be combined with some type
of passive filtering. The passive filter is there to absorb the harmonic currents while the
active filter blocks the transfer of harmonics to the rest of the PS. Details of this
combination will be covered in hybrid filter. Meanwhile the SAPF’s main function is to
reduce or cancel the harmonic currents produced by the non-linear load by injecting a
compensating current into the utility system. Figure 2.3 showed the configuration of a shunt
active filter where it is connected in parallel to the non-linear loads.
Figure 2.3: Single phase shunt active filter configuration
The filter above consists of four power electronic switches which produce an output
current that will be injected to the PS for harmonic compensation. The switches are
controlled by an integrated circuit. A lot of control methods have been studied by past
10
researchers, which includes neural network, instantaneous p-q theory (instantaneous
reactive power theory), synchronous d-q reference frame theory, fast Fourier transform
technique (FFT) etc. Among all, the most commonly used due to their accuracy, robustness
and simple calculation are the p-q and d-q theory [14].
The p-q theory is implemented to control a single phase SAPF in [15]. The block
diagram of the implemented SAPF controller using p-q theory is shown in Figure 2.4. The
designed control system is then implemented on the ATMEL NGW100 development board
to ensure simultaneous real-time acquisition of voltage and current data.
Figure 2.4: Block diagram of SAPF controller using p-q theory
Similar approach using p-q theory to control an SAPF has also been conducted on
[16]. The proposed filter is designed to improve PF and generate harmonics current
compensation. The SAPF controller which is based on p-q theory has been proven to be a
powerful tool through experimental results. The set-up is also simple enough to allow
digital implementation using a standard and inexpensive 16-bits microcontroller
(Intel 80296SA) with minimum additional hardware.
In [17], a d-q theory is used instead to control the 3 phase voltage source converter
(VSC) based SAPF. This method was chosen because it has greater and better performance
when the supply voltage is distorted. The main difference of this method from p-q theory
is that the d-q method requires the determination of the angular position of the synchronous
reference of the source voltages. Phase locked loop (PLL) algorithm is used in this research
to determine the angular position and a decoupled controller is used to generate the required
firing pulses to the SAPF. The d-q based SAPF simulated in MATLAB/Simulink was
capable in compensating the reactive power and thus mitigate harmonics.
The d-q theory has also been implemented on a VSC based SAPF in [18]. The only
difference with [17] was that, the filter designed used sinusoidal pulse width modulation
11
(SPWM) to generate the required firing pulses to the SAPF switches. This research has also
proven the capability of d-q based SAPF in mitigating harmonics.
It is critical to decide the most suitable control method to mitigate harmonics on a
PS. A study conducted on [19] evaluates the performance of a 3 phase 3 wire SAPF using
both p-q theory and d-q theory under distorted supply and non-linear load conditions. The
SAPF performance under both control methods were validated using MATLAB/Simulink.
Based on the simulation result, p-q theory gives a better approach than d-q theory for
compensation of harmonic currents and thus improving THD.
Other than the common control method, a novel control method introduced in [20]
have successfully employed SAPF to mitigate harmonics distortion while also improving
the PF. The methods, namely proposed control algorithm (PCA) and conventional control
algorithm (CCA) were carried out and the result have shown that both control methods
improved the PF up to 0.982 while keeping the total demand distortion (TDD) within an
acceptable level. Another novel control method called sinusoidal current control strategy
(SCC) was developed in [21]. This control method was modified from the p-q theory. The
main advantage of this new method is that it can also be applied to unbalanced supply
condition.
2.2.4 Hybrid active power filters (HAPF)
This filter combines both active and passive shunt filters. There are many possible
combinations in hybrid filter design like the single tuned hybrid active power filter (STHF)
and double tuned hybrid active power filter (DTHF) as shown in Figure 2.5. Hybrid filters
provide a viable alternative to the use of active filters only, since the unit may be sized to
only a fraction of the total compensating power [22], thus limiting the overall cost.
(a) (b)
Figure 2.5: (a) STHF, (b) DTHF in 3-phase distribution system [23]
12
The effectiveness of a HAPF has been studied in [22] to dampen harmonic
resonance caused by PFCC as well as to mitigate harmonics voltages and currents in
industrial PS. It is a combination of a small rated active filter and a 5th tuned passive filter,
which are connected in series. The hybrid filter was developed with the assumption that
only the 5th harmonics voltage exists at PCC. Figure 2.6 shows the system configuration.
Figure 2.6: Hybrid filter system set-up
When harmonics resonance occurs, a substantial 5th harmonic current (IF5) will flow
into the passive filter. To avoid the passive filter from absorbing the excessive current, the
active filter which has also detected the overcurrent across the passive filter will adjusts its
gain K to be greater than zero. Among the three different harmonic detection methods
employed by the active filter, the harmonic current through the passive filter (IFh) detecting
method is substantially stable and accurate compared to the other two mainly because the
ratio of the extracted harmonic component is the highest. IFh detecting method is applied on
the PS to further study the impact of an active filter in dampening harmonics resonance in
a hybrid filter operation. The PS was set with an initial 2.3% 5th harmonic voltage at VBUS.
When both filters were disconnected, the 5th harmonic voltage appearing on the VBUS was
magnified by 6.3 due to harmonic resonance versus 2.7 magnification factor when only the
passive filter was installed. Next, the hybrid filter was installed and the result have shown
that the filter was able to reduce the 5th harmonic voltage appearing at VBUS to one-sixth of
the voltage produced when only the passive filter is used. The above result was achieved
with the active filter designed at a required rating of less than 1% of the rated load.
A broader performance criterion of hybrid filters was studied in [23] whereby it
focuses on comparing the performance of STHF against DTHF. The filters were tested
under the same loading conditions and control method in order to compare its performance
13
in terms of THD, PFC and the power processed by the converter. The end result have shown
that both performed well in mitigating THD and PFC. However, in terms of active power
processed, 3rd harmonic mitigation and neutral current reduction, DTHF managed to
outperform STHF.
2.2.5 Phase shifting method
Apart from the methods mentioned earlier, PFC and harmonics mitigation can also be done
using phase shifting approach [5]. The research is focused on solving power harmonics
problem related to 3 phase diode-bridge rectifiers commonly used as input stage in low
voltage VSDs. The method proposed involves capturing harmonics generated from
separate sources, shifting one source of harmonics 180o with respect to the other source and
then adding them together. Equal harmonic amplitudes will result in harmonics
cancellation. The experimental set-up consists of 2 identical VSDs, which were fed by
separate power transformers with phase shifted output voltages as shown in Figure 2.7.
This technique under certain conditions eliminates dominant 5th and 7th current harmonics,
achieved THD below IEEE 519 limits and thus leading to an improvement of the PS PF i.e.
PF close to unity achieved at PCC2.
Figure 2.7: Phase shifting approach for VSDs PFC and harmonics mitigation
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2.3 PF Correction (PFC)
PF is the ratio of the active power (working power, P) to the apparent power (total power
delivered by the utility or consumed by the load, S). A low PF means that only a fraction
of the total power delivered or consumed is used to do the actual work while the rest is
consumed by the reactive components of the load. The relationship between apparent power
(S), active power (P) and reactive power (Q) is shown in Figure 2.8 where φ is the phase
difference between supply voltage and current.
Figure 2.8: Relationship between S, P and Q
The most common way to correct PF is by adding shunt capacitors in parallel with
the loads. Usually they are placed at the PCC. The best way to visualize how capacitors
correct PF is by using the power triangle shown in Figure 2.9.
Figure 2.9: Addition of capacitors to correct PF
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2.4 IEEE Standard for Harmonic Control
IEEE Standard 519-2014 [24] specifies the recommended line-to-neutral harmonic voltage
limits as shown in Table 2.1. All values should be in percent of the rated frequency voltage
at PCC.
Table 2.1: Voltage distortion limit
Bus voltage V at PCC Individual harmonic (%) Total harmonic
distortion THD (%)
V ≤ 1 kV 5.0 8.0
1 kV ˂ V ≤ 69 kV 3.0 5.0
69 kV ˂ V ≤ 161 kV 1.5 2.5
161 kV ˂ V 1.0 1.5a
aHigh voltage systems can have up to 2.0% THD where the cause is an HVDC
terminal whose effects will have attenuated at points in the network where future
users may be connected.
Meanwhile the recommended current distortion limits for systems nominally rated
120 V through 69 kV, for systems nominally rated above 69 kV through 161 kV and for
systems nominally rated above 161 kV are shown in Table 2.2, 2.3 and 2.4 respectively.
The TDD usage is similar to THD except that the distortion is expressed as a percent of the
maximum demand load current instead of as a percent of the fundamental current
magnitude. TDD is defined in Eq. 2.1.
= ∑ () × 100% (2.1)
where is the rms value of individual harmonic current, is the maximum rms demand
current and ℎ is the harmonic order.
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Table 2.2: Current distortion limits for system rated 120 V through 69 kV
Maximum harmonic current distortion in percent of IL
Individual harmonic order (odd harmonics)a,b
ISC / IL 3 ≤ h ˂ 11 11 ≤ h ˂ 17 17 ≤ h ˂ 23 23 ≤ h ˂ 35 35 ≤ h ˂ 50 TDD
˂ 20c 4.0 2.0 1.5 0.6 0.3 5.0
20 ˂ 50 7.0 3.5 2.5 1.0 0.5 8.0
50 ˂ 100 10.0 4.5 4.0 1.5 0.7 12.0
100 ˂ 1000 12.0 5.5 5.0 2.0 1.0 15.0
˃ 1000 15.0 7.0 6.0 2.5 1.4 20.0
Table 2.3: Current distortion limits for system rated above 69 kV through 161 kV
Maximum harmonic current distortion in percent of IL
Individual harmonic order (odd harmonics)a,b
ISC / IL 3 ≤ h ˂ 11 11 ≤ h ˂ 17 17 ≤ h ˂ 23 23 ≤ h ˂ 35 35 ≤ h ˂ 50 TDD
˂ 20c 2.0 1.0 0.75 0.3 0.15 2.5
20 ˂ 50 3.5 1.75 1.25 0.5 0.25 4.0
50 ˂ 100 5.0 2.25 2.0 0.75 0.35 6.0
100 ˂ 1000 6.0 2.75 2.5 1.0 0.5 7.5
˃ 1000 7.5 3.5 3.0 1.25 0.7 10.0
Table 2.4: Current distortion limits for system rated above 161 kV
Maximum harmonic current distortion in percent of IL
Individual harmonic order (odd harmonics)a,b
ISC / IL 3 ≤ h ˂ 11 11 ≤ h ˂ 17 17 ≤ h ˂ 23 23 ≤ h ˂ 35 35 ≤ h ˂ 50 TDD
˂ 25c 1.0 0.5 0.38 0.15 0.1 1.5
25 ˂ 50 2.0 1.0 0.75 0.3 0.15 2.5
≥ 50 3.0 1.5 1.15 0.45 0.22 3.75
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CHAPTER 3
METHODOLOGY
3.1 Introduction
This chapter describes modeling of a 3 phase distribution system with non-linear load and
PFCC, passive filter and SAPF using PSCAD software. This chapter also includes
mathematical equations of PFCC and passive filter.
3.2 Circuit topology
The 3 phase distribution system is formed by a balanced 3 phase source, a non-linear load
and PFCC. The SAPF consists of 6 controllable semiconductor switches with their
antiparallel diodes, and also an energy storage element, DC link capacitor (Cdc). An RLC
passive filter is also connected to the PCC. Figure 3.1 illustrates the circuit topology.
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Figure 3.1: Passive filter and SAPF topology
The application of PFCC on the power system may cause harmonic resonance as a
result of a series resonance between capacitive reactance of PFCC and the inductive
reactance of the source. Therefore, the RLC passive filter was tuned to the harmonic
resonance frequency of the non-linear load to absorb the harmonic current resonance
arising from the non-linear load. Meanwhile, the SAPF injects compensation currents to
the power system to reduce/eliminate the overall harmonic components to prevent
harmonic current propagation to the source.
3.3 Design circuit elements
3.3.1 Distribution system
The 3 phase source modeled is 400V, 20kVA, 50Hz while the non-linear load consists of a
3 phase 6-pulse bridge rectifier using 6 thyristors and an RL load as shown in Figure 3.2.
In practical, most DC drives use the 6-pulse bridge rectifier due to its relatively simple
control systems [1].
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Figure 3.2: Distribution system
The firing angle, of the thyristors is varied between 0 to 60o [25]. Due to the
presence of source inductance , the current commutation through the thyristors cannot
change instantaneously. Thus during the commutation angle , all four thyristors are
conducting simultaneously. The commutation process reduces the average load voltage
. From Eq. (3.1), the following relationship for the commutation angle is obtained,
where is the load current.
( + ) = () − 2 √2 (3.1)
As the source modeled has of 0.0005H, the expression for the average load
voltage is given by Eq. (3.2), where is source line to line voltage and is the
fundamental frequency.
= 3√2# cos() − 3 # (3.2)
In many applications, a load with series inductance results in a load current that is
essentially DC [26]. For a DC load current, the AC line current '( of the bridge rectifier
can be expressed in terms of its Fourier components as per Eq. (3.3), where ) is the source
fundamental frequency. The line currents consists harmonics of order 6k ± 1, k = 1,2,3…
20
'((+) = 2√3# ,cos( )+) − 15 cos(5 )+)+ 17 cos(7 )+) − 111 cos(11 )+) + 113 cos(13 )+) − ⋯0
(3.3)
3.3.2 PFCC
PF of the system is given by Eq. (3.4), where 1, 1, are the fundamental rms voltage,
fundamental rms current and supply rms current respectively,
34 = 35 = 11 cos(61 − 71)1 = 1 cos(61 − 71) 34 = 8'+9+':;<+9 × 8'=><?@?:+34 (3.4)
The distortion factor (DF) is defined as the ratio of 1to . Since DPF can never be
greater than unity, the PF of a non-linear system has an upper bound defined by DF.
Referring to Figure 2.5, the required capacity of PFCC is given by Eq. (3.5), where AB is
the compensating reactive power in kVAR, 3 (kW) is the active power absorbed by the
system, 6)C as the initial PF angle and 6DEF, the desired or final PF angle.
PFCC in kVAR, AB = 3tan(6)C − 6DEF) (3.5)
Old PF angle, 6)C = J1(34)C × 1) (3.6)
Final PF angle, 6DEF = J1(34DEF × 1) (3.7)
3.3.3 Passive filter
The passive filter consists of a resistor, inductor and capacitor connected in series. An ideal
single tuned filter is said to be tuned on the frequency D, that makes its inductive and
capacitive reactance to be equal.
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Tuned frequency, D = 1√K (3.8)
The sharpness of filter tuning is determined by the quality factor A, and is defined
as the ratio of inductance (or capacitance) LD, to resistance M, at resonant frequency (Eq.
(3.9)). Thus, higher Q can be achieved with smaller M. Typical values of A fluctuate
between 15 and 80 for filters that are used in the industry. Low voltage filters (480 to 600V)
are associated with low A values while medium voltage filters (4.16 to 13.8kV) have A
values in the upper range [27-28].
Quality factor, A = LDM (3.9)
For a filter tuned to harmonic :, the reactance of inductor and capacitor is expressed
in Eq. (3.10), where is the inductance, K is the capacitance and D is the harmonic
frequency. The value of and K can be calculated using Eq. (3.11) and (3.12).
Reactance, LD = D = 1 DK (3.10)
Substituting Eq. (3.10) into (3.9),
= MA D (3.11)
K = 1MA D (3.12)
3.3.4 SAPF
The SAPF is modeled using 6 gate turn-off thyristors (GTO). GTO is selected as it only
requires a pulse for switching thus simplifying the SAPF control. The DC link capacitor is
used to supply a constant input current to the SAPF. In this simulation, the DC link
capacitor is represented by an ideal DC voltage source with rated voltage of 400kV. The
ideal voltage source will provide any active power required in simulation, meaning that it
is capable of supplying an infinite amount of energy for an infinite amount of time.
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3.4 Control techniques
3.4.1 Calculation of reference compensations currents
3.4.1.1 PQ theory
The instantaneous and reactive power method, p-q theory approach has been implemented
in this project. The process flowchart using p-q theory is illustrated in Figure 3.3.
Figure 3.3: Calculation of current reference based on p-q theory
Load current and voltage measurement
Clarke transformation (Calculate α-β voltage and current) Eq. (3.13) and (3.14), Figure 3.4
Calculate instantaneous real power, p and reactive power, q
Eq. (3.15), Figure 3.5
High pass filter for px calculation Eq. (3.18)
High pass filter for qx calculation Eq. (3.18)
Compensation currents calculation Eq. (3.16), Figure 3.6
Inverse Clarke transformation Eq. (3.17), Figure 3.7
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The p-q theory consists of a Clarke transformation of the 3 phase system voltages
((, N, B) and load currents ((, N, B) in the a-b-c coordinates to the α-β coordinates as
expressed by Eq. (3.13) and (3.14) and demonstrated by Figure 3.4.
OPQ = R23STTU1 −12 −120 √32 −√32 VW
WXY(NB Z (3.13)
OPQ = R23STTU1 −12 −120 √32 −√32 VW
WXY(NBZ (3.14)
(a) Vα calculation (b) Vβ calculation
(c) Iα calculation (d) Iβ calculation
Figure 3.4: PSCAD models for Clarke transformation
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After the transformation, p-q theory instantaneous power components are calculated
using Eq. (3.15), where = is the instantaneous real power, and [ is the instantaneous
imaginary power. Figure 3.5 shows the corresponding PSCAD model.
\=[] = O P−P Q OPQ (3.15)
(a) p calculation (b) q calculation
Figure 3.5: PSCAD models for p-q instantaneous power components calculation and
HPF to obtain px and qx
Each of the active and reactive power is composed of continuous and alternating
terms. The continuous term corresponds to the fundamental current and voltage. The
alternating part represents power related to the sum of the harmonic components of current
and voltage. In order to calculate the reference compensation currents that the active filter
should inject, it is necessary to separate the desired power components from the undesired
ones denoted by =^ and [^. Specifically, a high pass filter (HPF) is used in this project to
separate the desired power components from the undesired ones [3.5]. The undesired power
components are used to determine the compensation currents in the α-β coordinates as per
Eq. (3.16) while Figure 3.6 shows the corresponding PSCAD model.
OBBPQ = 1 + P O −PP Q \=^[^] (3.16)
(a) Icα calculation (b) Icβ calculation
Figure 3.6: PSCAD models for compensation current calculation in α-β coordinates
